Minimum Cuts of Distance-Regular Digraphs.

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph F, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of F is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular-digraph F with diameter D = 2, degree k <= 3 or A = 0 (A is the number of 2-paths from u to v for an edge uv of F) is super vertex-connected, that is, any minimum vertex cut of F is the set of all out-neighbors (or in-neighbors) of a single vertex in F. These results extend the same known results for the undirected case with quite different proofs.